The results in the literature are not conclusive regarding the relationships between the strength of concrete and the particle size and type of coarse aggregates used in concrete production. Furthermore, few studies have used wave propagation to analyse these relationships. Therefore, this research used ultrasonic and static compression tests to evaluate the influences of these factors on the elastic parameters of 81 concrete test specimens produced with two maximum sizes of conventional coarse aggregates (9.5 mm and 12.5 mm) and lightweight aggregates (expanded clay). The ultrasonic testing results showed that the elastic parameters (longitudinal elastic modulus (E) and transverse elastic modulus (G)) were influenced by the type and size of the coarse aggregates; these influences were not detected in the static compression testing results. The results of the ultrasonic and static compression tests showed that the Poisson ratio was not influenced by the type or size of the coarse aggregates.